Plotting "Terrain" with "Water" on them Using BarChart3D

Question

It's easy to present a terrain using BarChart3D using ChartLayout -> "Grid"with the following code:

terrain = {{10, 10, 10, 10, 10, 10, 10, 10}, {10, 10, 6, 6, 4, 7, 10, 
    10}, {10, 10, 7, 10, 5, 10, 10, 10}, {10, 10, 7, 6, 5, 10, 2, 
    1}, {10, 10, 8, 10, 10, 10, 10, 10}, {10, 9, 8, 6, 4, 5, 2, 
    1}, {10, 10, 10, 5, 10, 10, 10, 10}, {10, 6, 1, 4, 1, 1, 1, 
    1}, {10, 6, 6, 3, 2, 1, 1, 1}, {10, 10, 10, 10, 10, 10, 10, 10}};
BarChart3D[terrain, ChartLayout -> "Grid", 
 Method -> {"Canvas" -> None}, ColorFunction -> "TemperatureMap", 
 BoxRatios -> {7, 10, 3}, ChartStyle -> [email protected], 
 ViewPoint -> {1.3, 1.2, 4.}, ImageSize -> 300, PlotRange -> {0, 10}]

It's also easy to present the height of the water flowing on this terrain by a similar code:

water = {{0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 3, 3, 5, 2, 0, 0}, {0, 
    0, 2, 0, 4, 0, 0, 0}, {0, 0, 2, 3, 4, 0, 0, 0}, {0, 0, 1, 0, 0, 0,
     0, 0}, {0, 1, 1, 1, 2, 1, 1, 1}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0,
     4, 1, 1, 1, 1, 1}, {0, 0, 0, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 
    0, 0}};
BarChart3D[water, ChartLayout -> "Grid", 
 Method -> {"Canvas" -> None}, ColorFunction -> "TemperatureMap", 
 BoxRatios -> {7, 10, 3}, ChartStyle -> [email protected], 
 ViewPoint -> {1.3, 1.2, 4.}, ImageSize -> 300, PlotRange -> {0, 10}]

But I would love to have a graph that shows both information: The terrain shall lay below the waterflow with 100% opacity. They should be colored just like the first code do. However, the water shall have a 30% opacity and colored blue. In this way, we can get the information of terrain as well as water elegantly in one chart with one glimpse.

However, ChartLayout->"Stacked" can put different layers together, but only in 2-D format, while ChartLayout->"Grid" cannot stack different layers. Their simple combination won't work too.

So, put it simple, my question is: how can we "Stack" a "Grid" using BarChart3D?

Thanks!

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Edit

Actually I would love to put the water "on" the terrain, so it should look like the following picture, but terrain and water shall have different color:

I gave out an solution in my answer, but I would still love to have one using mainly BarChart3D cause it is a more direct form I think.

---

Update2

Thanks everyone for providing so many elegant solution, so there's only one question left:

As you can see, Using "Grid" layout we can get a 2D+height.graph. Meanwhile, using "Stacked" layout we can get stacked result. But why there're no easy way to use them together? It seems that this will not be a hard work for Wolfram as both functionality already exist......

Answer 1

Update

Using @kglr suggestions to overcome Histogram3D's ColorFunction limitation.

Histogram3D[
 Flatten[MapIndexed[ConstantArray[#2, #1] &, #, {2}], 2] & /@ {terrain, water},
 Automatic, "Count",
 ChartLayout -> "Stacked", ChartStyle -> {Opacity[1], Blue}, 
 ChartElementFunction -> {ChartElementDataFunction[
    "GradientScaleCube", "ColorScheme" -> "Rainbow"], Automatic}]

---

Unfortunately Histogram3D will not take a list of colour functions for its ColorFunction option. Therefore the most I can do is make the ground Brown and the water Blue.

Histogram3D[
 Flatten[MapIndexed[ConstantArray[#2, #1] &, #, {2}], 2] & /@ {terrain, water},
 Automatic, "Count",
 ChartLayout -> "Stacked",
 ChartStyle -> {Opacity[1, Brown], Blue}]

Hope this helps.

Answer 2

You can easily add the water matrix to the terrain matrix (and zero it where there is no water):

t = ListPlot3D[terrain, InterpolationOrder -> 0, 
   ColorFunction -> "TemperatureMap", Mesh -> None, Filling -> 0, 
   FillingStyle -> Gray, PlotRange -> All, BoundaryStyle -> None];
w = ListPlot3D[(terrain + water)*Sign[water], InterpolationOrder -> 0, 
   PlotStyle -> {[email protected], Blue}, PlotRange -> All, Mesh -> None, 
   Filling -> 0, FillingStyle -> {[email protected], Blue}, BoundaryStyle -> None];
Show[t, w]

The same with BarChart3D:

t = BarChart3D[terrain, PlotRange -> All, ChartLayout -> "Grid", 
   Method -> {"Canvas" -> None}, BarSpacing -> {0, 0}, 
   ColorFunction -> "TemperatureMap", BoxRatios -> {7, 10, 3}, 
   ChartStyle -> {EdgeForm@"TemperatureMap"}, 
   ImageSize -> 300, PlotRange -> {0, 10}];
w = BarChart3D[(terrain + water)*Sign@water, PlotRange -> All, 
   ColorFunction -> (Lighter@Blue &), ChartLayout -> "Grid", 
   Method -> {"Canvas" -> None}, BarSpacing -> {0, 0}, 
   BoxRatios -> {7, 10, 3}, ChartStyle -> {[email protected]}, 
   ImageSize -> 300, PlotRange -> {0, 10}];
Show[t, w]

An alternative, if the water has an even surface level:

Show[g1, Graphics3D[{[email protected], EdgeForm@None, Blue, 
  Cuboid[{1, 1, 0}, {8, 10, 15}]}], ImageSize -> 500, Boxed -> False]

Answer 3

It seems the plot is more informative if (1) the bars are thinner and more transparent, and (2) there is a tooltip showing a 2D BarChart with stacked layout.

{n, m} = Dimensions[terrain];
{cx, cy} = {1/4, 1/4};
Graphics3D[{
  Red, Opacity[0.1], Cuboid[{1/2, 1/2, 0}, {n + 1/2, m + 1/2, 0}],
  Table[Tooltip[{
     Red, Opacity[0.1], 
     Cuboid[{i, j, 0}, {i + cx, j + cy, terrain[[i, j]]}],
     Blue, Opacity[0.3], 
     Cuboid[{i, j, terrain[[i, j]]}, {i + cx, j + cy, 
       terrain[[i, j]] + water[[i, j]]}]},
    BarChart[Transpose[{terrain[[i]], water[[i]]}], 
     PlotLabel -> Row[{"row:", i}], ChartLayout -> "Stacked"]
    ], {i, n}, {j, m}]}, Axes -> True, Boxed -> False, 
 BoxRatios -> {n/Max[n, m], m/Max[n, m], 1/3}, ImageSize -> Large]

XKCD update

The answer of Simon Woods made me think that we should look and the XKCD versions of the plots.

Answer 4

You can do it with Cuboid

Graphics3D[{Opacity[0.5], {l, w} = Dimensions[water]; 
 Table[{Blue, Cuboid[{i, j, 0}, {i + 1, j + 1, water[[i, j]]}]}, {i,l}, {j, w}],
 wmax = Max[water];
 Opacity[0.2], {l, w} = Dimensions[terrain];
  tscale = 1/3; (*scale terrain height for better look*)
 Table[{Red, Cuboid[{i, j, wmax}, {i + 1, j + 1, 
        wmax + terrain[[i, j]]tscale}]}, {i, l}, {j, w}]
}]

You can control the distance between water and terrain by changing wmax manually.

Using ColorSchemes

Graphics3D[{Opacity[0.8], {l, w} = Dimensions[water];
 wmin = Min[water]; wmax = Max[water];
 Table[{ColorData["Rainbow"][(water[[i, j]] - wmin)/(wmax - wmin)], 
 Cuboid[{i, j, 0}, {i + 1, j + 1, water[[i, j]]}]}, {i, l}, {j, w}],
 base = wmax; (*gap between water and terrain*)
 Opacity[0.2], {l, w} = Dimensions[terrain];
 tscale = 1/3;(*scale terrain height for better look*)
 tmin = Min[terrain]; tmax = Max[terrain];
 Table[{ColorData["DarkRainbow"][(terrain[[i, j]] - tmin)/(tmax - tmin)], 
  Cuboid[{i, j, base}, {i + 1, j + 1, 
  base + terrain[[i, j]] tscale}]}, {i, l}, {j, w}]}]

Changing Opacity with height

For terrain

Graphics3D[{
{l, w} = Dimensions[terrain];
tscale = 1/3;(*scale terrain height for better look*)
tmin = Min[terrain]; tmax = Max[terrain];
Table[{fx = (terrain[[i, j]] - tmin)/(tmax - tmin); 
ColorData["DarkRainbow"][fx], Opacity[1 - fx + 0.1], 
EdgeForm[None], 
Cuboid[{i, j, base}, {i + 1, j + 1, 
  base + terrain[[i, j]] tscale}]}, {i, l}, {j, w}]}]

Answer 5

Here are alternatives (which OP did not ask for). But OP requests graphs with which

[...] we can get the information of terrain as well as water elegantly in one chart with one glimpse.

• The mosaic plot shows the conditional probabilities of the terrain-vs-water values, and that is easy to grasp information. Easier, actually, than looking into stacked 3D bar plots.

• The Chernoff faces, are mostly for fun, but they do show outliers in the data, which, are not easy to see in the plots of the rest of the answers, or the plot in OP's question.

Mosaic plot

This is over flattened data, has the advantage of showing the conditional probabilities of the terrain-water values:

Import["https://github.com/antononcube/MathematicaForPrediction/blob/master/MosaicPlot.m"]

MosaicPlot[Transpose[{Flatten@terrain, Flatten@water}], 
 "ColumnNames" -> {"terrain", "water"}, 
 ColorRules -> {1 -> Reverse[ColorData[12, "ColorList"]]}, ImageSize -> Large]

Note that the coloring corresponds to terrain values.

Chernoff faces

The data has to be (column) normalized for this plot. The face length depends on the terrain. The vertical position of the eyes and eye size depend on the water. The face color depends on the normalized terrain-water pairs. The grid has the same structure as the original 2D arrays for terrain and water.

Import["https://raw.githubusercontent.com/antononcube/\
MathematicaForPrediction/master/ChernoffFaces.m"]

data = N@Transpose[{Flatten@terrain, Flatten@water}];
Grid[Partition[
  MapThread[
   ChernoffFace[<|"FaceLength" -> #[[1]], 
      "EyesVerticalPosition" -> #[[2]], "EyeSize" -> #[[2]], 
      "FaceColor" -> 
       Blend[{Lighter@Brown, Lighter@Blue}, #2[[2]]/Total[#2]]|>, 
     ImageSize -> 60] &, {VariablesRescale@data, data}],
  Length@First@terrain], Dividers -> All]

Answer 6

Graphics3D[{Opacity[1], {l, w} = Dimensions[water];
  MapIndexed[{Hue[#/10], 
     Cuboid[{#2[[1]], #2[[2]], 0}, {#2[[1]] + 1, #2[[2]] + 1, #}]} &, 
   terrain, {2}],
  Opacity[0.2], Blue, 
  MapIndexed[
   If[#[[2]] != 0, 
     Cuboid[{#2[[1]], #2[[2]], #[[1]]}, {#2[[1]] + 1, #2[[2]] + 
        1, #[[1]] + #[[2]]}], Nothing] &, 
   Thread /@ Thread[{terrain, water}], {2}]}, 
 BoxRatios -> {1, 1, .3}]

This code will generate a proper result.(Despite its color is not in rainbow form) But I would still love to have an answer using BarChart3D.